The head of the government's education watchdog prompted an angry reaction from Muslim leaders yesterday after claiming that the growth of Islamic faith schools posed a challenge to the coherence of British society.

In a deliberate intervention criticised as "irresponsible" and "derogatory" by senior Muslim representatives, the chief inspector of schools David Bell claimed that a traditional Islamic education did not equip Muslim children for living in modern Britain.

Diversity and acceptance of different cultures was potentially a great strength, Mr Bell claimed, but it could also undermine "our coherence as a nation" if taken to extremes.

Mr Bell used a speech about citizenship to the Hansard Society - an educational charity which promotes effective parliamentary democracy - to explore how youngsters determine their "national identity" through the teaching of citizenship in schools. He turned to the fast-growing independent faith school sector - which includes about 100 Muslim, 100 evangelical Christian and 50 Jewish schools, broadening his argument to say: "Faith should not be blind. I worry that many young people are being educated in faith-based schools, with little appreciation of their wider responsibilities and obligations to British society."

The new figures on independent faith schools are contained in Ofsted's new annual report, which will be published early next month and which will say that many Muslim schools "must adapt their curriculum to ensure that [they provide] pupils with a broad general knowledge of public institutions and services in England and help them to acquire an appreciation of and respect for other cultures in a way that promotes tolerance and harmony".

Mr Bell said: "The growth in faith schools needs to be carefully but sensitively monitored by government to ensure that pupils at all schools receive an understanding of not only their own faith but of other faiths and the wider tenets of British society. We must not allow our recognition of diversity to become apathy in the face of any challenge to our coherence as a nation ... I would go further and say that an awareness of our common heritage as British citizens, equal under the law, should enable us to assert with confidence that we are intolerant of intolerance, illiberalism and attitudes and values that demean the place of certain sections of our community, be they women or people living in non-traditional relationships."

The role of single faith schools in the British education system has long been controversial. Last year a report from a group of Muslim academics and educationalists urged ministers to fast-track some Muslim schools into the state system, claiming that "institutional racism" was preventing the government from setting up Muslim state schools from scratch. Those in the state sector do well. Last week the country's first all girls' Islamic state secondary school, Feversham College in Bradford, came top of the national league tables for "value-added" performance at GCSE.

In his speech Mr Bell said that "traditional Islamic education does not entirely fit pupils for their lives as Muslims in modern Britain". He also warned that diversity should not be interpreted as separation or segregation.

Last night Dr Mohamed Mukadam, chairman of the Association of Muslim Schools, accused Mr Bell of Islamophobia and challenged him to a public debate on the issue. Mr Mukadam, who is also principal of Leicester Islamic Academy, which has 700 pupils aged five to 16, said: "I am very surprised to hear Mr Bell's comments and I challenge him to come up with evidence that Muslim schools are not preparing young people for life in British society. It's a misconception of Islamic schools and a further example of Islamophobia. For a person in his position to make such a generalised comment just beggars belief."

Iqbal Sacranie, secretary general of the Muslim Council of Britain, said: "The issue of community cohesion and coherence is of paramount importance for the whole nation but we consider it highly irresponsible to suggest that the growth of Muslim faith schools poses a threat to 'our coherence as a nation'. The issue around schools not adequately fulfilling their responsibility in preparing children for their wider responsibility is a generic issue affecting all poorly resourced schools." At present there are more than 100 Muslim schools, teaching the equivalent of about 3% of Muslim children, but only five of them receive state funding.

Dr Mohammad Naseem, the chairman of Birmingham's Central Mosque, said: "Muslims schools do not harm social cohesion and neither do Jewish or Christian schools. Why he is picking up on Muslim schools I do not understand. Why would teaching children the principles of their faith affect community cohesion? It's unfortunate that he has made these comments."

But Idris Mears, of the Association of Muslim Schools, said: "One of the things the Association of Muslim Schools is doing is to get schools participating in the community. I don't think it's unfair of Mr Bell to bring the matter up. Muslim schools are aware of it."